KCET · Maths · Limits
\(\lim _{x \rightarrow 1} \frac{\tan \left(x^{2}-1\right)}{x-1}\) is equal to
- A 2
- B \(\frac{1}{2}\)
- C \(-2\)
- D \(\frac{-1}{2}\)
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
We have, \(\lim _{x \rightarrow 1} \frac{\tan \left(x^{2}-1\right)}{x-1} \quad\left(\frac{0}{0}\right.\) form \()\) \(=\lim _{x \rightarrow 1} \frac{\sec ^{2}\left(x^{2}-1\right) \cdot 2 x}{1}\)
[using L'Hospital's rule] \(=2 \cdot \sec ^{2}(0)=2\)
[using L'Hospital's rule] \(=2 \cdot \sec ^{2}(0)=2\)
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